Fritz David Carlson (23 July 1888 – 28 November 1952) was a

Swedish Swedish or ' may refer to: Anything from or related to Sweden, a country in Northern Europe. Or, specifically: * Swedish language, a North Germanic language spoken primarily in Sweden and Finland ** Swedish alphabet, the official alphabet used by ...

mathematician A mathematician is someone who uses an extensive knowledge of mathematics in their work, typically to solve mathematical problems. Mathematicians are concerned with numbers, data, quantity, mathematical structure, structure, space, Mathematica ...

whose work on

analytic function In mathematics, an analytic function is a function that is locally given by a convergent power series. There exist both real analytic functions and complex analytic functions. Functions of each type are infinitely differentiable, but complex ...

s and

geometry Geometry (; ) is a branch of mathematics concerned with properties of space such as the distance, shape, size, and relative position of figures. Geometry is, along with arithmetic, one of the oldest branches of mathematics. A mathematician w ...

left a lasting mark on twentieth-century mathematics. After the death of

Torsten Carleman Torsten Carleman (8 July 1892, Visseltofta, Osby Municipality – 11 January 1949, Stockholm), born Tage Gillis Torsten Carleman, was a Swedish mathematician, known for his results in classical analysis and its applications. As the director of t ...

, he headed the

Mittag-Leffler Institute The Mittag-Leffler Institute (Swedish: Institut Mittag-Leffler) is a mathematical research institute in Sweden. Located in Djursholm, a suburb of Stockholm, it invites scholars to participate in half-year programs in specialized mathematical su ...

Life and career

Born in

Vimmerby Vimmerby () is a city and the seat of Vimmerby Municipality, Kalmar County, Sweden with 10,934 inhabitants in 2010. Overview Stångån is a small river running through the city. Vimmerby had its charter as early as the fourteenth century. The ...

on 23 July 1888, Fritz David Carlson completed his secondary schooling at

Linköping Linköping ( , ) is a city in southern Sweden, with around 167,000 inhabitants as of 2024. It is the seat of Linköping Municipality and the capital of Östergötland County. Linköping is also the episcopal see of the Diocese of Linköping (Chu ...

in 1907 and went on to earn his doctorate at

Uppsala University Uppsala University (UU) () is a public university, public research university in Uppsala, Sweden. Founded in 1477, it is the List of universities in Sweden, oldest university in Sweden and the Nordic countries still in operation. Initially fou ...

in 1914 with a thesis on a class of

Taylor series In mathematics, the Taylor series or Taylor expansion of a function is an infinite sum of terms that are expressed in terms of the function's derivatives at a single point. For most common functions, the function and the sum of its Taylor ser ...

whose

coefficient In mathematics, a coefficient is a Factor (arithmetic), multiplicative factor involved in some Summand, term of a polynomial, a series (mathematics), series, or any other type of expression (mathematics), expression. It may be a Dimensionless qu ...

s vary analytically with the index. He was appointed professor of descriptive geometry at the Royal Institute of Technology in Stockholm in 1920 and in 1928 took up the chair of higher analysis at the Stockholm College of Advanced Studies. From 1930 he served on the editorial board of ''

Acta Mathematica ''Acta Mathematica'' is a peer-reviewed open-access scientific journal covering research in all fields of mathematics. According to Cédric Villani, this journal is "considered by many to be the most prestigious of all mathematical research journ ...

'', and after the death of

in early 1949 he was entrusted with the administration of the

Djursholm Djursholm () is one of four suburban districts in, and the seat of Danderyd Municipality, Stockholm County, Sweden. Djursholm is included in the multi-municipal Stockholm urban area. Djursholm is divided into a number of different areas: Djursho ...

. Carlson's research ranged from the arithmetic properties of

power series In mathematics, a power series (in one variable) is an infinite series of the form \sum_^\infty a_n \left(x - c\right)^n = a_0 + a_1 (x - c) + a_2 (x - c)^2 + \dots where ''a_n'' represents the coefficient of the ''n''th term and ''c'' is a co ...

Dirichlet series In mathematics, a Dirichlet series is any series of the form \sum_^\infty \frac, where ''s'' is complex, and a_n is a complex sequence. It is a special case of general Dirichlet series. Dirichlet series play a variety of important roles in anal ...

(an

infinite series In mathematics, a series is, roughly speaking, an addition of infinitely many terms, one after the other. The study of series is a major part of calculus and its generalization, mathematical analysis. Series are used in most areas of mathemati ...

with applications in

number theory Number theory is a branch of pure mathematics devoted primarily to the study of the integers and arithmetic functions. Number theorists study prime numbers as well as the properties of mathematical objects constructed from integers (for example ...

) and the

Riemann zeta function The Riemann zeta function or Euler–Riemann zeta function, denoted by the Greek letter (zeta), is a mathematical function of a complex variable defined as \zeta(s) = \sum_^\infty \frac = \frac + \frac + \frac + \cdots for and its analytic c ...

(a function closely tied to the distribution of

prime number A prime number (or a prime) is a natural number greater than 1 that is not a Product (mathematics), product of two smaller natural numbers. A natural number greater than 1 that is not prime is called a composite number. For example, 5 is prime ...

s), yielding theorems that remain standard references. He also authored a three-volume Swedish textbook series on elementary and spatial geometry (published 1943–48) and for thirty years acted as examiner for the Swedish secondary-school baccalaureate examination.

Hans Rådström Hans Vilhem Rådström (1919–1970) was a Swedish mathematician who worked on complex analysis, continuous groups, convex sets, set-valued analysis, and game theory. From 1952, he was ''lektor'' (assistant professor) at Stockholm University, ...

Germund Dahlquist Germund Dahlquist (16 January 1925 – 8 February 2005) was a Sweden, Swedish mathematician known primarily for his early contributions to the theory of numerical analysis as applied to differential equations. Dahlquist began to study mathematics ...

, and Tord Ganelius were among his students. Carlson's contributions to

analysis Analysis (: analyses) is the process of breaking a complex topic or substance into smaller parts in order to gain a better understanding of it. The technique has been applied in the study of mathematics and logic since before Aristotle (38 ...

include

Carlson's theorem In mathematics, in the area of complex analysis, Carlson's theorem is a uniqueness theorem which was discovered by Fritz David Carlson. Informally, it states that two different analytic functions which do not grow very fast at infinity can not co ...

, the Polyá–Carlson theorem on rational functions, and Carlson's inequality: :

\left( \sum_^\infty , a_n, \right)^4 \leq \pi^2  \sum_^\infty , a_n, ^2 \, \sum_^\infty n^2 , a_n, ^2~.

References

{{DEFAULTSORT:Carlson, Fritz David 1888 births 1952 deaths 20th-century Swedish mathematicians Academic staff of the KTH Royal Institute of Technology Mathematical analysts Directors of the Mittag-Leffler Institute People from Vimmerby Municipality